Minds On
Purchasing a property
Purchasing a home today requires a down payment of 20%. A down payment is the money paid at the time of purchase. The rest of the purchase price can be borrowed from a bank or other financial institution. This type of loan is a mortgage.
The cost of borrowing money is the amount of interest paid on the loan. The total you will pay on the loan is not only the rate of interest, but also how long it takes you to pay the loan.
The longer it takes you to pay back the money you borrow, the more you will pay in interest. This period of time to pay back the loan is the amortization.
Brainstorm a list of items that could require a down payment and a loan in order to purchase the item.
Action
Amortization periods
The chart details the monthly mortgage payment and the interest costs for the full amortization. The length of the amortization period has an impact on both of these figures. It is important to be aware that the total interest costs increase significantly if the amortization period exceeds 25 years.
| Details | 25-Year Amortization | 30-Year Amortization |
|---|---|---|
| Mortgage principal | $150,000.00 | $150,000.00 |
|
Monthly mortgage payment (principal and interest, 5 yr Term @ 4.00%) |
$789.04 |
$713.28 |
|
Interest costs for full amortization |
$86,707.04 |
$106,779.45 |
Source – Royal Bank of Canada
Chart summary
Choosing the longer 30-year amortization would reduce your monthly mortgage payment by $75.76. This may be beneficial in the short-term, but you would also pay an additional $20,072.41 in total interest costs over the full amortization compared to the 25-year amortization.
Comparing total interest payments
The amount of interest paid on a mortgage can vary significantly and is dependent on the amortization period and the interest rate. The three tables below provide information for 15-year, 20-year, and 25-year amortization. Each table outlines the monthly payment, total repaid, and total interest payment for four different interest rates.
15-year Amortization (paid back over 15 years)
| Interest rate | Monthly payment | Total repaid | Total interest payment |
|---|---|---|---|
| 4% | $443.81 | $79,886 | $19,886 |
| 6% | $506.31 | $91,136 | $31,137 |
| 8% | $573.39 | $103,210 | $43,210 |
| 10% | $644.76 | $116,057 | $56,057 |
20-year Amortization (paid back over 20 years)
| Interest rate | Monthly payment | Total repaid | Total interest payment |
|---|---|---|---|
| 4% | $363.59 | $87,262 | $27,261 |
| 6% | $429.86 | $103,166 | $43,166 |
| 8% | $501.86 | $120,446 | $60,447 |
| 10% | $579.01 | $138,962 | $78,963 |
25-year Amortization (paid back over 25 years)
| Interest rate | Monthly payment | Total repaid | Total interest payment |
|---|---|---|---|
| 4% | $316.70 | $95,010 | $35,011 |
| 6% | $386.58 | $115,974 | $55,974 |
| 8% | $463.09 | $138,927 | $78,927 |
| 10% | $545.22 | $163,566 | $103,566 |
Interest rate and amortization calculations
If you would like, you can complete the next series of word problems using TVO Mathify. You can also use your notebook or the following fillable worksheet.
Task #1
The three Amortization tables are for a $60,000.00 loan over 15 years, 20 years, and 25 years. Calculate the difference of the total interest payment from
- 15-years amortization at 4%, 6%, 8% and 10%
- 20-years amortization at 4%, 6%, 8% and 10%
- 25-years amortization at 4%, 6%, 8% and 10%
15-year Amortization
| Interest rates being compared | Difference in total interest payment |
|---|---|
| 4% and 6% | |
| 6% and 8% | |
| 8% and 10% |
20-year Amortization
| Interest rates being compared | Difference in total interest payment |
|---|---|
| 4% and 6% | |
| 6% and 8% | |
| 8% and 10% |
25-year Amortization
| Interest rates being compared | Difference in total interest payment |
|---|---|
| 4% and 6% | |
| 6% and 8% | |
| 8% and 10% |
Task #2
Complete the 30-year Amortization schedule for $60,000.00 using the same interest rates: 4%, 6%, 8%, 10%. You can use an online mortgage calculator like saving.org
- determine the total repaid amount for 4%
- determine the total repaid amount for 6%
- determine the total repaid amount for 8%
- determine the total repaid amount for 10%
30-year Amortization for $60,000.00
| Interest rate | Monthly payment | Total repaid |
|---|---|---|
| 4% | $ | $ |
| 6% | $ | $ |
| 8% | $ | $ |
| 10% | $ | $ |
Task #3
Two friends are looking to purchase a new home. They are doing some research before buying to determine the impact of different interest rates.
They have found a new one-bedroom condo in downtown Toronto and have been pre-approved for a mortgage.
- The condo costs $945,000.
- They have saved 20% for a down payment- $189,000.
- Chef has saved 20% for a down payment
They have been approved by two banks.
Here is what was offered:
Bank A: Pre-approved at 2.38% interest rate on a 25-year fixed mortgage
Bank B: Pre-approved at 2% interest rate on a 30-year fixed mortgage
Bank A
Step 1
Calculate the dollar amount that they need to borrow from the bank for the mortgage. (cost of the condo- the down payment) Use an online mortgage calculator to determine the monthly payment for a 25-year fixed mortgage at 2.38% interest rate.
| Down payment as a % | 20% of $945,000 |
| Down payment in dollars | $189,000 |
| Mortgage (cost of new condo – down payment) | $ |
| Monthly mortgage payment | $ |
Step 2
How much total interest will they pay over the course of the mortgage? (Hint: You will need to locate the “Amortization Schedule” or “Amortization”)
| Total interest paid over 25 years with 20% down | $ |
Bank B
Step 1
Calculate the dollar amount that they need to borrow from the bank for the mortgage. (cost of the condo- the down payment) Use an online mortgage calculator to determine the monthly payment for a 30-year fixed mortgage at 2% interest rate.
| Down payment as a % | 20% of $945,000 |
| Down payment in dollars | $189,000 |
| Mortgage (cost of new condo – down payment) | $ |
| Monthly mortgage payment | $ |
Step 2
How much total interest will they pay over the course of the mortgage? (Hint: You will need to locate the “Amortization Schedule” or “Amortization”)
| Total interest paid over 30 years with 20% down | $ |
| Difference between interest paid (20% versus 25%) | $ |
Friend A said it’s obvious what they should do. They should go with the lower interest rate because they will pay less on the money they borrow.
Friend B said they should go for the higher interest rate because they will have the mortgage paid back sooner.
Compare the total interest paid over 30 years at 2% with the total interest paid over 25 years at 2.38%.
Consider the monthly mortgage payment for each plan.
Explain which deal you think the friends should take. Justify your thinking. Be sure to include your calculations of total interest paid and monthly mortgage payments to support your reasoning.
Press the ‘TVO Mathify’ button to access this resource and the ‘Activity’ button for your note-taking document.
TVO Mathify (Opens in new window) Activity(Open PDF in a new window)Capital gains
Task: Taxable income, investments, and capital gains
Income at both the provincial and federal level is taxed at different rates, dependent on gross income. The table depicts the province of Ontario tax rates for 2020. Refer to the table to answer the questions.
Government of Canada, Ontario 2020 Tax Rates
| Rate | Income bracket |
|---|---|
| 5.05% | On first $44,740 of taxable income |
| 9.15% | On next $44,742 |
| 11.16% | On next $60,518 |
| 12.16% | On next $70,000 |
| 13.16% | On the amount over $220,000 |
Source: CRA provincial tax rates (Ontario)
If you would like, you can complete the next series of questions using TVO Mathify. You can also use your notebook or the following fillable worksheet.
Press the ‘TVO Mathify’ button to access this resource and the ‘Activity’ button for your note-taking document.
TVO Mathify (Opens in new window) Activity(Open PDF in a new window)
A banker purchased a condominium in downtown Toronto as an investment property. They have been renting out the property for eleven years. They purchased the property for $347,000.00 and just recently sold it for $863,000.00.
1. The banker’s total income is $83,465.00. Using the Ontario Tax table, calculate how much they will pay in income tax.
| Total employment income | $83,465.00 |
| Income tax paid at 5.05% | $ |
| Income tax paid at 9.15% | $ |
| Total income tax paid | $ |
2. In Canada, 50% of capital gains is taxable and added to your total income amount. Calculate the amount of capital gains that the banker will be responsible for paying taxes on due to the sale of the investment property.
| Purchase price | $347,000.00 |
| Selling price | $863,000.00 |
| Difference (selling price – purchase price) | $ |
| Capital gains | $ |
3. Does the taxable capital gains added to the banker’s income move them to a higher tax rate?
4. What will the banker’s new taxable income be?
| Income due to employment | $83,465.00 |
| Income due to capital gains | $ |
| New taxable income | $ |
Consolidation
Reflecting on interest rates and capital gains
Reflect on what you have learned about interest rates and capital gains to create a one-page information pamphlet for others who are new to these concepts.
Be sure to include:
You can record and display your information in a method of your choice
Reflection
As you read the following descriptions, select the one that best describes your current understanding of the learning in this activity. Press the corresponding button once you have made your choice.
I feel...
Now, expand on your ideas by recording your thoughts using a voice recorder, speech-to-text, or writing tool.
When you review your notes on this learning activity later, reflect on whether you would select a different description based on your further review of the material in this learning activity.
If you would like, you can complete this activity using TVO Mathify. You can also use your notebook or the following fillable worksheet.
Connect with a TVO Mathify tutor
Think of TVO Mathify as your own personalized math coach, here to support your learning at home. Press ‘TVO Mathify’ to connect with an Ontario Certified Teacher math tutor of your choice. You will need a TVO Mathify login to access this resource.
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